1. Field of the Invention
This invention relates to a method of and an apparatus for canceling echoes included in a signal, and more particularly to a method of and apparatus for canceling the echoes of a transmission signal which are derived from a plurality of reception signals and include such echoes in an overlapping relationship.
2. Description of the Related Art
In a system which receives a plurality of reception signals and outputs one or more transmission signals independent of the reception signals, echoes from such reception signals are sometimes mixed into the transmission signal or signals. For example, in a multi-channel television conference system, a plurality of microphones are used in order to pick up speech of a speaker, and a plurality of loudspeakers are provided, in the system on the other side, corresponding to the respective microphones. Accordingly, a plurality of reception signals acquired by the microphones are received from the other side, and such reception signals are reproduced by the respective loudspeakers. Consequently, the microphones in the system will pick up, in addition to the speech of a speaker on one side, a plurality of reception signals from the other side. In this instance, since such reception signals are propagated as sounds in the space between the loudspeakers and microphones, they will be mixed as echoes into signals to be transmitted from the microphones to the other side (that is, transmission signals). Mixture of an echo of a reception signal Into a transmission signal may be similarly caused by crosstalk and so forth.
Mixture of an echo from a reception signal into a transmission signal causes the quality of the transmission signal to deteriorate and, when the transmission signal is speech, significantly Impairs speech clarity and intelligibility. Therefore, there have been repeated attempts to cancel echoes of a transmission signal from a reception signal. When a single reception signal is received, cancellation of echoes is a comparatively easy technique and is in practical use. Cancellation of echoes derived from a plurality of reception signals has so far been attempted by two multi-channel echo canceling methods: one employs an apparatus of the serially connected type, and the other employs an apparatus of the linear combiner type.
FIG. 1 shows, in a block diagram, the construction of a multi-channel echo canceling apparatus of the serially connected type for use with a system for two channels of transmission and reception signals.
In the system shown, a first reception signal 501 inputted from the outside is reproduced by a first loudspeaker 503, and similarly a second reception signal 502 is reproduced by a second loudspeaker 504. First and second transmission signals 512 and 513, which are speech uttered by a speaker 511, are inputted to first and second microphones 509 and 510, respectively. Here, the loudspeakers 503 and 504, microphones 509 and 510 and speaker 511 are in the same acoustic space and acoustically coupled to one another. Consequently, to the first transmission signal 512, a first echo 505 (which is derived from the first reception signal 501 reproduced by the first loudspeaker 503 and coming to the first microphone 509 by way of a spatial acoustic path) and a second echo 506 (which is derived from the second reception signal 502 reproduced by the second loudspeaker 504 and coming to the first microphone 509) are added together. A first mixed signal 514, including the first transmission signal 512 and the echoes 505 and 506, is obtained from the first microphone 509. Similarly, a third echo 507 from the first reception signal 501 and a fourth echo 508 from the second reception signal 502 are added to the second transmission signal 513, and consequently, a second mixed signal 515 of the second transmission signal 513 with the echoes 507 and 508 is obtained from the second microphone 510.
The serially connected multi-channel echo canceling apparatus 520 includes four adaptive filters 521 to 524 and four subtracters 525 to 528. The apparatus 520 cancels the first and second echoes 505 and 506 of the first mixed signal 514 and the third and fourth echoes 507 and 508 of the second mixed signal 515 in the manner described below.
In particular, in order to cancel the echoes 505 and 506 mixed in the first mixed signal 514, a pseudo echo (echo replica) corresponding to the first echo 505 is first produced by the first adaptive filter 521 to which the first reception signal 501 is inputted, and the echo replica is then subtracted from the first mixed signal 514 by the first subtracter 525. The first adaptive filter 521 has filter coefficients which are controlled so as to minimize the output of the first subtracter 525. Another echo replica corresponding to the second echo 506 is then produced by the second adaptive filter 522 to which the second reception signal 502 is inputted, and the echo replica is subtracted from the output of the first subtracter 525 by the second subtracter 526. The second adaptive filter 522 similarly has filter coefficients which are controlled so as to minimize the output of the second subtracter 526. The output of the second subtracter 526 is produced as the first output signal 516 of the serially connected multi-channel echo canceling apparatus 520. Upon echo cancellation, the first adaptive filter 521 and first subtracter 525 and the second adaptive filter 522 and second subtracter 526 may otherwise be reversed in order to remove the second echo 506 first.
Similarly, in order to cancel the echoes 507 and 508 mixed in the second mixed signal 515, an echo replica corresponding to the third echo 507 is first produced by the third adaptive filter 523 to which the first reception signal 501 is inputted, and the echo replica is subtracted from the second mixed signal 515 by the third subtracter 527. The third adaptive filter 523 has filter coefficients which are controlled so as to minimize the output of the third subtracter 527. Another echo replica corresponding to the fourth echo 508 is then produced by the fourth adaptive filter 524 to which the second reception signal 502 is inputted, and the echo replica is subtracted from the output of the third subtracter 527 by the fourth subtracter 528. The fourth adaptive filter 524 similarly has filter coefficients which are controlled so as to minimize the output of the subtracter 528. The output of the fourth subtracter 528 is produced as the second output signal 517 of the echo canceling apparatus 520. Upon echo cancellation, the third adaptive-filter 523 and third subtracter 527 and the fourth adaptive filter 524 and fourth subtracter 528 may otherwise be reversed in order to remove the fourth echo 508 first. The echoes 505 to 508 of the first and second mixed signals 514 and 515 are canceled in this manner, and signals after such cancellation are the first and second output signals 516 and 517 and are outputted from the echo canceling apparatus 520.
A multi-channel echo canceling apparatus of the linear combiner type is shown in FIG. 2. Referring to FIG. 2, the echo canceling apparatus 530 shown cancels echoes 505 to 508 mixed in mixed signals 514 and 515 in a manner similar to the one described above. The echo canceling apparatus 530 thus includes four adaptive filters 531 to 534 and two subtracters 539 and 540. The echo canceling apparatus 530 operates in the following manner to cancel the echoes 505 to 508 of the first and second mixed signals 514 and 515 and output signals after such echo cancellation as first and second output signals 516 and 517.
In particular, in order to cancel the echoes 505 and 506 mixed in the first mixed signal 514, an echo replica 535 corresponding to the first echo 505 is first produced by the first adaptive filter 531 to which the first reception signal 501 is inputted, and another echo replica 536 corresponding to the second echo 506 is produced by the second adaptive filter 532 to which the second reception signal 502 is Inputted. The echo replicas 535 and 536 corresponding to the first and second echoes 505 and 506, respectively, are subtracted from the first mixed signal 514 by the first subtracter 539. The first and second adaptive filters 531 and 532 have filter coefficients which are controlled so as to minimize the output of the first subtracter 539. The output of the first subtracter 539 is produced as the first output signal 516 of the echo canceling apparatus 530.
In order to cancel the echoes 507 and 508 mixed in the second mixed signal 515, the first reception signal 501 is inputted to the third adaptive filter 533, by which an echo replica 537 corresponding to the third echo 507 is produced, and the second reception signal 502 is inputted to the fourth adaptive filter 534, by which another echo replica 538 corresponding to the fourth echo 508 is produced. The echo replicas 537 and 538 corresponding to the third and fourth echoes 507 and 508, respectively, are subtracted from the second mixed signal 515 by the second subtracter 540. The third and fourth adaptive filters 533 and 534 are controlled so as to minimize the output of the second subtracter 540. The output of the second subtracter 540 is produced as the second output signal 517 of the echo canceling apparatus 530.
We will now examine the operation of the conventionally proposed multi-channel echo canceling apparatus described above. First, we investigate a multi-channel echo canceling apparatus of serially connected type shown in FIG. 1. In this apparatus, the output of the first subtracter 525 includes the second echo 506 which cannot be canceled by a echo replica from the first adaptive filter 521. The step size of the first adaptive filter 521 must be extremely small because of this second echo 506 interfering the convergence of the first adaptive filter 521. As result, the convergence of the first adaptive filter 521 becomes very slow. And the accuracy of the convergence goes bad because of the existence the high level interfering signal. The rate and accuracy of the convergence of the second adaptive filter 522 respectively becomes slow and bad, too, because the rate and accuracy of the convergence of the first adaptive filters respectively are slow and bad. The same result similarly applied to the both third and fourth adaptive filters 523 and 524.
One of the principal applications of such multi-channel echo canceling apparatus is in multi-channel television conference systems. In this type of system, a speaker's speech picked up simultaneously by a plurality of microphones causes reception signals from the other side. Accordingly, each of the reception signals has an attenuation amount and a time delay basically corresponding to the distance between the speaker and the microphone, and the reception signals of the channels have very strong cross-correlations. Therefore, the following analysis proceeds on the assumption that, in the linear combiner type multi-channel echo canceling apparatus shown in FIG. 2, the second reception signal 502 is equivalent to a signal obtained by delaying the first reception signal 501, echo paths which can be approximated to a transversal filter, and an adaptive transversal filter is employed for the adaptive filters 531 to 534.
The first and second reception signals 501 and 502 at a time n are represented by x.sub.1 (n) and x.sub.2 (n), respectively, and the echo mixed In the first mixed signal 514 is represented by d(n). When the time difference between the first and second reception signals 501 and 502 is represented by n.sub.d (n.sub.d : integer, n.sub.d .gtoreq.0), EQU x.sub.2 (n)=x.sub.1 (n-n.sub.d) (1)
For the simplification, it is assumed that all of the spatial acoustic paths from the first and second loudspeakers 503 and 504 to the first and second microphones 509 and 510 have an equal impulse response length, and the impulse response length is represented by N, the impulse response of the spatial acoustic path from the first loudspeaker 503 to the first microphone 509 is represented by h.sub.1,i, and the impulse response of the spatial acoustic path from the second loudspeaker 504 to the first microphone 509 is represented by h.sub.2,i. Thus, the echo d(n) is given by ##EQU1## Substituting equation (1) into equation (2) to cancel x.sub.2 yields ##EQU2## An echo replica d(n) to be produced by adding the output of the first and second adaptive filters 531 and 532 is given when the i-th weighting coefficients of the first and second adaptive filters 531 and 532 are represented by w.sub.1,i (n) and w.sub.2,i (n), respectively, by ##EQU3## Substituting equation (1) into equation (4) to cancel x.sub.2 (n), yields ##EQU4## Consequently, the residual echo e(n) is given by ##EQU5## From equation (6), the requirements by which echoes can be canceled completely are given by ##EQU6## From equation (7), it can be seen that w.sub.1,0 (n), . . . , w.sub.1,n.sbsb.d-1 (n) and w.sub.2,N-n.sbsb.d (n), . . . , w.sub.2,N-1 (n) are determined decisively, but w.sub.1,n.sbsb.d (n), . . . , w.sub.1,N-1 (n) and w.sub.2,0 (n), . . . , w.sub.2,N-n.sbsb.d.sub.-1 (n) each have an indefinite number of solutions.
Incidentally, an adaptive filter is controlled by a known controlling method which is based on the LMS (least-mean-square) algorithm or on a learning method. Details of the LMS algorithm are disclosed, for example, in B. Widrow et al., "Adaptive Noise Canceling: Principles and Applications", Proc. of IEEE, Vol. 63, No. 12, pp.1692-1716, December 1975 (hereinafter referred to as reference 1). Meanwhile, details of such learning methods are disclosed, for example, in J. Nagumo and A. Noda, "A Learning Method for System Identification", IEEE Trans. on Automatic Control, Vol. AC-12, No. 3, pp.282-287, June 1967 (hereinafter referred to as reference 2). It is to be noted that a learning method is sometimes called a learning identification method or normalized LMS (NLMS).
Here, it is assumed that the LMS algorithm is used to control the adaptive filters 531 and 532, and for simplification of description, the adaptive filters 531 and 532 have the same step size and the reception signals are white noise. When the step size Is represented by .mu., the weighting coefficients of the adaptive filters 531 and 532 are updated as given respectively by EQU w.sub.1,i (n+1)=w.sub.1,i (n)+.mu.e(n)x.sub.1 (n-i) (8) EQU w.sub.2,i (n+1)=w.sub.2,i (n)+.mu.e(n)x.sub.1 (n-n.sub.d -i) (9)
Equation (6) is then substituted into equations (8) and (9) to obtain the mathematical expectation values for both sides.
First, when i=0, 1, . . . , n.sub.d -1, EQU E[w.sub.1,i (n+1)]=E[w.sub.1,i (n)]+.mu..sigma..sub.x.sup.2 {h.sub.1,i -E[w.sub.1,i (n)]} (10) EQU E[w.sub.2,N-i-1 (n+1)]=E[w.sub.2,N-i-1 (n)]+.mu..sigma..sub.x.sup.2 {h.sub.2,N-i-1 -E[w.sub.2,N-i-1 (n)]} (11)
where E[X] are the mathematical expectation values for the variable X, and .sigma..sub.x.sup.2 is the average power of the reception signals 501 and 502. Solutions to equations (10) and (11) are given respectively by EQU w.sub.1,i (n)=h.sub.1,i +(1-.mu..sigma..sub.x.sup.2).sup.n {E[w.sub.1,i (0)]-h.sub.1,i } (12) EQU w.sub.2,n-i-1 (n)=h.sub.2,N-i-1 +(1-.mu..sigma..sub.x.sup.2).sup.n {E[w.sub.2,N-i-1 (0)]-h.sub.2,N-i-1 } (13)
and they converge to optimum values when ##EQU7## The results of equations (12), (13) and (14) coincide with an ordinary LMS algorithm, that is, an LMS algorithm, when only one reception signal is involved. Otherwise, when i=n.sub.d, n.sub.d +1, . . . , N-1, EQU E[w.sub.1,i (n+1)]=E[w.sub.1,i (n)]+.mu..sigma..sub.x.sup.2 {h.sub.1,i -E[w.sub.1,i (n)]}+.mu..sigma..sub.2.sup.2 {h.sub.2,i-n.sbsb.d -E[w.sub.2,i-n.sbsb.d (n)]} (15) EQU E[w.sub.2,i-n.sbsb.d (n+1)]=E[w.sub.2,i-n.sbsb.d (n)]+.mu..sigma..sub.x.sup.2 {h.sub.1,i -E [w.sub.1,i (n)]}+.mu..sigma..sub.x.sup.2 {h.sub.2,i-n.sbsb.d -E{w.sub.2,i-n.sbsb.d (n)]} (16)
and their solutions are given respectively by EQU E[w.sub.1,i (n)]=h.sub.1,i +1/2{(1-2 .mu..sigma..sub.x.sup.2).sup.n +1} {E[w.sub.1,i (0)]-h.sub.1,i }+1/2{(1-2 .mu..sigma..sub.x.sup.2).sup.n -1} {E[w.sub.2,i-n.sbsb.d (0)]-h.sub.2,1-n.sbsb.d } (17) EQU E[w.sub.2,i-n.sbsb.d (n)]=h.sub.2,i +1/2{(1-2 .mu..sigma..sub.x.sup.2).sup.n +1} {E[w.sub.2,i-n.sbsb.d (0)]-h.sub.2,1-n.sbsb.d }+1/2{(1-2 .mu..sigma..sub.x.sup.2).sup.n -1} {E[w.sub.1,i (0)]-h.sub.1,i } (18)
Accordingly, when ##EQU8## they converge respectively to EQU E[w.sub.1,i (n)]=h.sub.1,i +1/2{E[w.sub.1,i (0)]-h.sub.1,i -1/2{E[w.sub.2,i-n.sbsb.d (0)]-h.sub.2,i-n.sbsb.d } (20) EQU E[w.sub.2,i-n.sbsb.d (n)]=h.sub.2,i +1/2{E[w.sub.2,i-n.sbsb.d (0)]-h.sub.2,i-n.sbsb.d }-1/2{E[w.sub.1,i (0)]-h.sub.1,i }(21)
In this instance, the maximum value of the step size is restricted to one half that of the case of an ordinary LMS algorithm, and consequently, the converging rate is slow and in addition the mathematical expectations do not converge to optimal values. Generally, when M channels of reception signals are involved, maximum values of the step sizes are restricted to 1/M of the values in the case of an ordinary LMS algorithm.
The first and second adaptive filters 531 and 532 used to cancel echoes mixed in the first mixed signal 514 have been examined above, and similar results are obtained with regard to the third and fourth adaptive filters 533 and 534. Further, while the LMS algorithm is employed as a controlling method for the adaptive filters, additional employment of the learning method results in convergence to the same values, and in this case as well, the step sizes are similarly restricted to a low level.
Thus, the multi-channel echo canceling methods and apparatus proposed to date that have been described above are disadvantageous in that, since the step sizes are restricted to a low level, convergence of the adaptive filter is slow, and the weighting coefficient of the adaptive filter does not converge to their optimum values. In particular, when the echo canceling methods and apparatus are applied to a multi-channel television conference system, the low converging rate is a very serious problem since the number of taps of adaptive filters is very great due to the fact that the principal cause of echoes is spatial acoustic propagation.